For question 1, the 5 is sitting outside there because it is a common number that can be divided out of each of those terms evenly, making the factoring easier in the end. When we divide 5 out of 5x^2, we are left with x^2. When we divide 5 out of 35x we are left with 7x, and when we divide 5 out of 60 we are left with 12. So the reduced or simplified polynomial is [tex]5(x^2-7x+12)[/tex]. The idea here now is to find 2 numbers that ADD up to -7 and MULTIPLY to positive 12. Those numbers are -3 and -4. Check the math. -4+(-3) = -7, and -4 * -3 = 12. So fill them into the parenthesis. 5(x-3)(x-4). That's question 1. For question 2, we have a perfect square binomial. That means that if we square the same (set of parenthesis) we will get back the original polynomial. 196, the leading coefficient in question 2 is a perfect square, with 14 being the square root. 25 is a perfect square with 5 being the square root. That means that (14x + 5)(14x + 5) will give us the original polynomial. FOIL it out to check it, but you'll be good.
